GridWits
Hard tier Technique 18 of 31 Used by Smart Hint

Cage Comparison

Compare two cages sharing a house and discard assignments that cannot coexist without repeating a digit.

How it works

  1. 1Two cages lie in one box. Cage A totals 12 in two cells: {3,9} or {4,8}. Cage B totals 8 in three: {1,2,5} or {1,3,4}.
  2. 2If B used {1,3,4}, A's {3,9} would repeat 3 in the box, while A's {4,8} would repeat 4.
  3. 3That B assignment has no compatible assignment for A, so discard it.
  4. 4B must use {1,2,5}; remove 3 and 4 from its cells. The solver performs the same check on live cell assignments when cages span more than one shared house.
Next in the ladder Naked Quad →

Four cells in a house between them using only four candidates lock those digits away from the rest.